Some Open Problems and New Tasks in Applied Mathematics

After the re-emancipation from pure mathematics in the latter part of the twentieth century, application-oriented mathematicians are now facing a wealth of new areas of activities and challenges for their research. This means that apart from individual open problems, two typical examples of which will be outlined here, applied mathematics is facing a lot of new tasks, from modelling practical situations in biology, medicine, nance and technology to providing tools for in silico experimentation and design. The resulting growing exposure of mathematicians to public interest implies a responsibility to keep standards of research high and to improve the endeavor for communicating among each other, to attract young people and to convince the general public of the usefulness and beauty of mathematics.